3 papers
math.DS2025
Herman's converse KAM mechanism revisited
Yi Liu, Lin Wang
In his celebrated counterexample to the KAM theorem, Herman introduced a perturbation of an integrable system consisting of two components: a hyperbolic term and a bump function. H…
math.DS2025
On Non-KAM Invariant Circles for Area-Preserving Twist Maps
Jiashen Guo, Yi Liu, Lin Wang
In this note, we investigate the dynamics of invariant circles in area-preserving twist maps. The invariant circles under consideration lie beyond the applicability of classical KA…
math.DS2025
Moser's twist theorem revisited
Yi Liu, Lin Wang
Inspired by the work of Katznelson and Ornstein, we present a short way to achieve the almost optimal regularity in Moser's twist theorem. Specifically, for an integrable area-pres…